Munich Personal RePEc Archive

Policy Measurement and Multilateral

Resistance in Gravity Models

Cipollina, Maria Pina and De Benedictis, Luca and Salvatici,

Luca and Vicarelli, Claudio

Università del Molise, Università di Macerata, Università Roma3,

ISTAT

November 2016

Online at https://mpra.ub.uni-muenchen.de/75255/

MPRA Paper No. 75255, posted 25 Nov 2016 10:18 UTC

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POLICY MEASUREMENT AND MULTILATERAL RESISTANCE IN

GRAVITY MODELS

Maria Cipollinaa, Luca De Benedictis

b, Luca Salvatici

c, Claudio Vicarelli

d

(NOVEMBER 2016)

ABSTRACT

Over the past decade, the gravity equation has emerged as the empirical workhorse in

international trade to study the ex-post effects of trade policies on bilateral trade. In this

paper we are concerned with the issue of how the econometric specification and the policy

measurement choices can affect the goal to obtain accurate estimates of the coefficient

associated with bilateral trade policies within a theoretically-consistent model. The problem

is even more serious when the policy treatment is approximated through dummies as it is still

often the case in the literature. Using a Monte Carlo simulation analysis, this paper shows

that the use of fixed effects to control for unobserved heterogeneity leads to biased estimates

of the policy impact even when the policy is measured through a continuous variable. The

bias highlighted by our results is the combination of measurement error about bilateral trade

costs (or preferences) and the specification used to proxy multilateral resistance terms.

KEYWORDS: Gravity model; Multilateral trade resistance; Policy evaluation; Monte Carlo

Analysis.

JEL CLASSIFICATION: C10; C50; F14

aUniversity of Molise, Via Francesco De Sancits 1, 86100 Campobasso, Italy.

Cipollina@unimol.itb

University Roma Tre, Italy. Dipartimento di Economia - Via Silvio D'Amico, 77 Roma

00145. debene@unimc.itcUniversity of Macerata, Via Crescimbeni 20, 62100 Macerata, Italy.

Luca.salvatici@uniroma3.itd

ISTAT, Italian National Insitute of Statistics, Via Cesare Balbo 16, 00184 Rome, Italy.

cvicarelli@istat.it

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1. Introduction

The gravity model has been used as a workhorse for analysing the determinants of

bilateral trade flows for 50 years since being popularized by Tinbergen (1962) and it

represents an important tool for the analysis of the effects of trade policies. In this paper, we

are concerned with two fundamental problems related to gravity-based estimates of the trade

impact of policies: multilateral trade resistance and policy measurement.

The first issue was emphasized by Anderson and van Wincoop (2003), whose work

presented what would become one of the most widely cited gravity models, showing that the

typical gravity equation should account for both “bilateral resistance,” e.g. the barriers to

trade between a pair of countries, and the so-called “multilateral resistance” term (MRT),

capturing the general equilibrium effect associated with the barriers to trade that each country

faces with all its trading partners. In its essence, what matters in explaining bilateral trade

flows are relative bilateral trade costs, and an omission of the MRT may lead to bias estimates

of the relevant elasticities.

The treatment of the multilateral resistance terms in gravity estimations has evolved over

the years and researchers have proposed various solutions (Piermartini and Yotov, 2016).

In order to overcome the computational difficulties of a structural estimation explicitly

expressing the exporter- and importer-specific terms as a function of the economic model’s

variables, as suggested by Anderson and van Wincoop (2003),1

many researchers have

approximated the MR by the so-called ‘remoteness indexes’ that are constructed as weighted

averages of bilateral distance, with Gross Domestic Products (GDPs) used as weights (see for

example Wei, 1996; and Baier and Bergstrand, 2009). Head and Mayer (2014) criticize such

reduced- form approaches as they “bear little resemblance to [their] theoretical counterpart.”

(p.150).2

Hummels (2001) and Feenstra (2004) advocate the use of directional (exporter and

importer) fixed effects in cross-section estimations, and the recommendation has been

extended from the cross-sectional setting to a longitudinal one in a static (Baldwin and

Taglioni, 2006; De Benedictis and Taglioni, 2011) or a dynamic context (De Benedictis and

1Fally (2015) demonstrates that gravity regressions with fixed effects and Poisson PML can be used as a simple

tool to solve the estimation problem raised by Anderson and van Wincoop (2003). Indeed, in the Poisson PML

specification the estimated fixed effects are consistent with the definition of outward and inward multilateral

resistance indexes and the equilibrium constraints that they need to satisfy.2

An alternative approach to handle the multilateral resistances is to simply eliminate these terms by using

appropriate ratios based on the structural gravity equation. Notable examples include Head and Ries (2001),

Head, Mayer and Ries (2010), and Novy (2013).

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Vicarelli, 2008; Olivero and Yotov, 2012): the MR terms should be accounted for by exporter-

time and importer-time fixed effects in a gravity estimation framework with panel data.

Structural estimators fully exploit the information on the data-generating process and are thus

potentially more efficient than other approaches. However, they require the underlying

economic model to be correctly specified.

In contrast, the fixed effects approach is to leave the fixed effects unspecified, being

consistent regardless of the nature of their dependence (Egger and Staub, 2016). Fixed effects

also avoid misspecification problems that could lead to spurious regressions. In particular,

fixed effects include all the possible time-invariant unobserved factors specifically affecting

bilateral trade flows in each country-pair: geographical, political, cultural, institutional

factors. Fixed effect method produces consistent estimates of average border effects across

countries; moreover, by replacing bilateral distances with importer-exporter fixed effects, it

avoids the shortcomings of distance as a measure of transport and information costs.3

In order to control for time-varying unobserved trade costs in gravity equations, Baltagi

et al. (2003) suggested a full interaction effects design to analyse bilateral trade flows

controlling for all sorts of unobserved heterogeneity. However, the exporter-time and

importer-time fixed effects will also absorb the size variables from the structural gravity

model as well as all other observable and unobservable country-specific characteristics which

vary across these dimensions, including various national policies. Finally, as for nonlinear

models concern, an important drawback of fixed effects estimators is that they suffer from the

incidental parameters problem. In the context of the gravity equation, this means that as the

number of observations grows, the number of parameters that has to be estimated grows as

well. In general, this implies that fixed effects coefficients cannot be estimated consistently

and, worse, the inconsistency passes over to the estimate of the main variables of interest

(Egger and Staub, 2016).

The second issue refers to the trade policy measurement. Although it is well known that

gravity type models using policy dummies are misspecified and lead to erroneous economic

inferences (Màtyàs, 1997; Stack, 2009; Hornok, 2011), the approximation of trade policy

3Geographic distance is usually proxied by kilometers between capital cities of exporting and importing

countries. This measure implicitly assumes that transport costs do not vary depending on transport mode, i.e.

overland and overseas transport costs are equal. Indeed, the straight-line distance assumes only one economic

center per country, but in fact a large country may have several economic centers.

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through dummies – even when the policy measure is inherently continuous - is still quite

common.4

The empirical literature emphasizes the importance of expressing trade policies through

continuous variables since they vary widely across products, importers and exporters, and at

least in the case of tariffs detailed data are currently available (De Benedictis and Salvatici,

2011). In this paper we consider preferential trade policies because differently by other

policies (e. g. trade creating effect of a custom union, of a free trade agreement or of a

currency unions that are measured by dichotomous dummy) can be measured through a

continuous variable.

The use of a simple dummy to capture the impact of preferential policies on trade is

inadequate because: (i) it confuses the policy implementation with all other factors that are

specific to the country-pair and are contemporaneous to the policy; (ii) it does not

discriminate among different policy instruments; (iii) it does not match the level of trade

barriers (Cardamone, 2011). Moreover, since country-time dummies tend to absorb too much

of the variation in the data, the heterogeneous policy effects are hardly identified.

The two issues, MRT and policy measurement, are related since trade policies have both

direct and indirect effects on trade: a reduction or increase in a tariff in a particular sector has

an effect on the price of goods in that sector but also in the rest of the economy, as a

consequence it affects the general equilibrium prices at home and abroad (Caliendo and

Parro, 2015). As a matter of fact, Egger and Staub (2016) show that predictions and average

marginal effects are functions not only of the direct coefficient but also of the fixed effects

estimates). Cipollina et al (2016) include in the preference margin definition policy the price

index consistent with the CES demand functional form. Moreover, they show that the policy

coefficient represents the elasticity of substitution: a crucial parameter in the debate about

impact of trade liberalization, which our results show how much is influenced by the

modelling choices in terms of MRT and policy measurement.

In this paper, we provide a quantitative assessment of the following proposition: the more

we control for the MTR and unobserved heterogeneity through a full set of fixed effects, the

less we are able to estimate the policy effect, and this is particularly true when the latter is

proxied by a dummy variable. As a consequence, the estimates of trade impact is biased.

4As a proxy for the existence of preferential trade agreements (PTA), many contributions to the gravity

literature use a “PTA dummy”. The quantitative survey by Cipollina and Pietrovito (2011) shows that the results

of the empirical analyses using a “PTA dummy” specification tend to overestimate the effect of the trade policy,

relatively to the results obtained by studies using some explicit measures of the preference margins.

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Our goal is to assess to what extent estimates of the impact of the policy treatment are

affected when all the cross sectional and time series heterogeneity is controlled for. Such an

assessment shows the possible consequences of compounding the error in measuring the

treatment (i.e., the policy variable) with a more or less complete specification of the fixed

effects structure.

To do this, we implement a data-generating-process and set up a Monte Carlo simulation

analysis that allows to control for the consequences of various fixed-effects specifications on

the estimated value of the parameter of interest (i.e., the policy impact).5

Our data-generating

process is built on an Heckman selection model. We show that the MRT fixed effects strategy

may not be appropriate when it is coupled with a measurement error in the policy variable.

Furthermore, through the simulation exercise we are able to precisely assess the

consequences of different possible fixed effects specifications of the gravity equation in the

presence of zero trade flows.

2. Gravity for Policies

The gravity model has been defined as the workhorse of international trade and its ability

to correctly approximate bilateral trade flows makes it one of the most stable empirical

relationships in economics (Leamer and Levinsohn 1995). Over the years there has been

dramatic progress both in understanding the theoretical basis for the equation and in

improving its empirical estimation (De Benedictis and Taglioni, 2011). Although for several

years these models has been thought of as a purely “empirical fact” reminiscent of Newton’s

law of universal gravitation, trade theorists have highlighted the fact that gravity-like

equations can be derived from several trade modelling frameworks (see Head and Mayer

(2014) for a survey, and Baltagi, Egger and Pfaffermayer (2015) for the empirical

counterparts of different theoretical models): CES product differentiation with imperfect

competition (Anderson, 1979; Bergstrand, 1985), Ricardian models (Eaton and Kortum,

2002), heterogeneous firms (Chaney, 2008; Helpman et al., 2008).

One of the traditional purposes of gravity equations has been to estimate the elasticity of

bilateral trade to various policies promoting trade, or to covariates capturing the “cost of

5In an influential article, Santos Silva and Tenreyro (2006) argued that gravity equations should be estimated in

their multiplicative form and use Monte Carlo simulations to compare the performance of nonlinear estimators

with that of ordinary least squares (in the log linear specification). Since then, the use of Monte Carlo analysis

has become increasingly common in gravity equation experiments (Santos Silva and Tenreyro, 2011; Martinez

Zarzoso, 2013; Bergstrand et al., 2013; Head and Mayer, 2014; Martin and Pham, 2014).

6

distance”. In this paper, we are interested in the wider use of the gravity equation: the ex-post

evaluation of the trade-enhancing effect of preferential trade policy. The trade cost is a

negative function of the preferential margin since trade preferences reduce border costs as a

consequence of tariff reduction. As in Cipollina et al (2010) we define the preferential margin

( , ) as the ratio between the reference tariff factor (1 + , ) and the applied tariff

factors faced by each exporter (1 + , ):

, =( , )

( , )(1)

In particular, the measure preference margin is expressed in relative rather than absolute

terms and this definition focuses on actual preferences with respect to possible competitors,

rather than measuring theoretical margins with respect to “bound” Most Favoured Nation

(MFN) tariffs (i.e., the ceiling set by the World Trade Organization (WTO) commitments).

The critical issue is the measurement of the reference tariff with respect to whom the

preference margin is determined. To account the advantage with respect to actual not

potential exporters, thus to avoid possible overestimation of the competitive advantages

enjoyed by exporting countries, we use as reference tariff the highest applied tariff factor.

The continuous policy variable quantifies the advantage granted with respect to other

importers: higher preferences decrease trade costs and, thus, reduce the negative trade impact

of the bilateral distance.

One of the most widely used specifications of a theory-based gravity equation is provided

by Anderson and van Wincoop (2003). In their formulation, bilateral trade flows between two

regions depend on the output of both regions and the bilateral trade costs relative to the trade

costs faced by the other regions, the so-called “multilateral resistance” term (MRT). The latter

term is defined as the sum of three components: (1) the bilateral trade barrier between region i

and region j, (2) i’s resistance to trade with all regions, and (3) j’s resistance to trade with all

regions. We argue that the most common way to handle the MRT in gravity models – namely

through the introduction of fixed effects – can be highly misleading since country-time-

product dummies are likely to absorb the variation in the variable representing the relevant

policy effect. This is confirmed by the results of Monte Carlo simulations, and the problem

turns out to be particularly serious when the policy treatment, which cannot be correctly

measured, is proxied through dummy variables.

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3. The Monte Carlo Simulation

To explore the performance of different modelling choices in finite samples, we set up a

Monte Carlo experiment. The questions that we seek to explore are how the estimate of the

policy impact is affected by the policy measurement, and by an increase in the number of

fixed effects.

3.1 The data-generating process

The data generating process consists of a structural part, including the bilateral-, exporter-,

and importer-specific determinants of exports; and a stochastic part, in which random errors

are drawn and joined to the structural part of exports.

Following the most recent literature highlighting the need to account for the variability of

trade policy at the tariff-line level (Baldwin and Taglioni, 2006; De Benedictis and Salvatici,

2011; Head and Mayer, 2014), this work is based on disaggregated data. The setup of the

Monte Carlo simulation includes 23 industrial sectors (ISIC Revision 2 Classification), 14

countries importing from 17 exporters, over the period 1998-2001. The dataset is built on

information provided by the TradeProd, TradePrices and the GeoDist Cepii databases

(http://www.cepii.fr/) on existing trade flows, production, expenditure, applied tariffs, import

and export price indices, distances between countries and dummies for contiguity, common

language, and former colonial links. Table A1 in the Appendix presents summary statistics.

The main weakness of the use of published data on price indexes is that existing price

indexes may not reflect true border effects accurately (Feenstra, 2002). However, this is not a

problem in our analysis, since trade flows are generated through the Monte Carlo simulation.

Starting from the initial dataset of 21,896 observations, we implement a data-generating-

process, replicated 10,000 times, using a standard bootstrap methodology, to draw a random

sample containing 5 importer countries, 10 products and 5 exporter countries over a period of

4 years. In each replication, the final dataset contains 1,000 observations that are manageable

in regressions with the full set of dummies.

We address the issue of zero flows by adopting the Heckman (1979) approach, assuming

that the selection equation contains at least one variable that is excluded from the behavioral

equation. We use equation (2) for the behavioral equation:

= ( ) + (2)

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where xi is a vector of explanatory variables; β is a vector of coefficient to be estimated;

and εi is the error term for observation i.

With a constant-elasticity functional form, almost always used, model estimated in levels

will have heavily skewed and heteroskedastic errors. We follow Santos Silva and Tenreyro

(SST)6

(2006) to design heteroskedastic error, and rewrite equation (2) in their formulation as

follows:

= ( ) ∗ (3)

with = 1 + ( )⁄ ,7 drawn as log normal random variable with mean 1 and

variance .

We add the following sample selection equation:

= ( ) ∗ ∗ (4)

where zi is the vector of explanatory variable in xi plus the regressor ( ) excluded from the

behavioural equation8. We follow Santos Silva and Tenreyro (SST) (2006) to design

heteroskedastic error, = 1 + ( )⁄ ,9 drawn as log normal random variable with

mean 1 and variance . The error term, ∗, in the sample selection equation is drawn as log

normal random variable with a correlation of 0.5 with .

We apply the selection rule to generate zeros of as follows: for with values less

than zero, replace with zero. For with values greater than zero, remains the same.

Coherently with the gravity equation, determinants of trade flows are:

( ) = ( + ln , + ln , − ln + + , + +

( − 1) ln , + ( − 1) ln , + ( − 1) lnΠ , + ) (5)

6Santos Silva and Tenreyro (2006) page 647.

7Rewriting = ( ) , where is a random variable statistically independent of , then the term

(equal to 1 + ) is statistically independent of , implying that the conditional variance of (and ) is

proportional to (2 ).8

The excluded restriction variable is generated as: = − [ ( ) ∗ ∗].9

With = ( ) , where is a random variable statistically independent of , then the term (equal to

1 + ) is statistically independent of , implying that the conditional variance of (and ) is proportional to

(2 ).

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where ⁄ is the importing country j’s share of the world spending on k; ⁄ is the

exporting country i’s share of the world’s sales of goods class k; Border, Language and

Colony are dummy variables taking the value of 1 for a pair of countries showing,

respectively, common border, language and colonial ties, and zero otherwise; > 1 is the

elasticity of substitution across goods in k; , is the preferential margin as eq.(1);

and Π are the MRTs; and Dt are time dummies.

All coefficients are set to 1 but the elasticity of substitution, σ, is set equal to 8, a value

within the range of the estimates included in the survey by Anderson and van Wincoop

(2004).

3.2 Simulations

After generating Trade flow ( , ) we use a Heckman two-step estimator with times

dummies, we estimate the following model:

ln( , ) = + ln , + ln , − ln + + , + +

( − 1) ln , + ( − 1) ln , + ( − 1) lnΠ , + + , , ( , ,

, , , , , , , , , , , , Π , , , ) (6),

and replicate each regression 10,000 times to get the set of = ( − 1) and its standard

errors. In the first column of Table 1 we show the statistics of the distribution of estimated

coefficients ( ) obtained using the continuous policy variable, ln , , assuming that all

variables in equation (6) are known (Model 1).

In Model 2 we drop the price indices, and Π , to confirm that the omission of the MRT

leads to biased estimates, estimating the following regression:

ln( , ) = + ln , + ln , − ln + + , + +

( − 1) ln , + + , , ( , , , , , , , ,

, , , , , ) (7).

Then, to proxy for the MRT we add different sets of fixed effects (FE):

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ln( , ) = + ln , + ln , − ln + + , + +

( − 1) ln , + + + , , ( , , , , , , , ,

, , , , , , ) (8).

Models from 3 to 7 differ in terms of the fixed effects structure, that is:

- Model 3 includes importer, exporter, and product dummies, i.e. = + + ;

- Model 4 includes importer-, and exporter-, product-specific dummies = + ;

- Model 5 adds to model 3 time invariant exporter-by-importer (bilateral) interaction effects

(Egger and Pfaffermayr, 2003), i.e., = + ;

- Model 6 includes importer and exporter time variant dummies in addition to the product-

specific dummies, i.e., = , + , + .

- Model 7 introduces the full-blown specifications including importer-, and exporter-,

product-specific time variant dummies, i.e. = , + , .

Independently from the presence of time-varying dummies, time dummies are included in all

models.

3.3 Results for preference margin

As expected, in model 1 of the estimated coefficient is = 7 that is the one assumed in

the data-generating process (Table 1). The estimated coefficient of the variable ln( , )

implies an elasticity of substitution equal to 8 (σ 7 + 1). The marked homogeneity of the

estimates is confirmed by the low value of the coefficient of variation (the ratio between the

standard deviation and the mean is around 0.8). Model 2 confirms that the omission of MRT

leads to biased estimates. The estimated coefficients are higher on average (7.67) and

statistically different from coefficients in Model 1. We use results of Model 1 as the

benchmark to assess the consequences of compounding the error in measuring the policy

variable with a more or less complete specification of the fixed effects structure (model 3-7).

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Table 1: Estimated coefficients of the policy variable: preference margin. The omission of

MRT

Policy Variable: ln (Pref kijt) MODEL 1 MODEL 2

Simple mean 7.00 7.67

Std. Deviation 0.58 1.24

Median 7.03 7.67

5th

percentile 6.06 5.78

95th

percentile 7.86 9.52

Notes: Statistics of the distribution of estimated coefficients obtained using Heckman two-step Model.

Dependent variable: ln (X , , ). All independent variables are specified in eq. (6). In model 2 multilateral price

indices are excluded (eq.(7)). Time Dummies included in all models. Simulations with 10.000 replications.

Table 2 shows the consequences of modelling the MRT with various structures of fixed

effects. In Model 3 we introduce time invariant exporter-, importer- and product-fixed effects:

the average of estimated coefficients of the policy variable is 7.09; in Model 4 we interact the

exporter and importer fixed effects with the product fixed effects and we get the average of

the estimated coefficients equal to 7.24; finally, specification of Model 5 adds the time

invariant bilateral fixed effects, as suggested by Egger and Pfaffermayr (2003), and leads to

the average result 7.14. These results differ significantly from Model 110

, and the higher

coefficients of variation imply a potentially large under/overestimation of the trade policy

impact. Surprisingly, the more complete structure of fixed effects does not improve the

performance of Model 2, since the addition of fixed effects does not seem to correct the bias

due to the omission of MRT, only reducing the overestimation on average. However, the

difference with respect to the benchmark is still significant, and this implies that working

with disaggregated data is better to control for the (unobserved) product heterogeneity than

for the bilateral one.

10For each model we employ a t-test to test the null hypothesis that the difference between the means of

parameter of interest is equal to zero. We reject the null hypothesis in all experiments.

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Table 2: Estimated coefficients of the policy variable: preference margin with FE

Policy Variable: ln (Pref kijt) Time- invariant FE Time- varying FE

MODEL 3 MODEL 4 MODEL 5 MODEL 6 MODEL 7

Simple mean 7.09 7.24 7.14 6.71 -3.53

Std. Deviation 0.70 1.40 0.90 0.75 932.95

Median 7.10 7.22 7.13 6.72 8.72

5th

percentile 5.95 5.14 5.70 5.47 -112.77

95th

percentile 8.22 9.45 8.58 7.90 119.63

Importer Yes

Exporter Yes

Product Yes Yes Yes Yes

Importer*Product Yes

Exporter*Product Yes

Importer*Exporter Yes

Importer*time Yes

Exporter*time Yes

Importer*product*time Yes

Exporter*product*time Yes

Notes: Statistics of the distribution of estimated coefficients obtained using Heckman two-step Model.

Dependent variable: ln (X , , ). All independent variables are specified in eq. (8). Time Dummies included in all

models. Simulations with 10.000 replications.

Model 6 and Model 7 represent the (in principle) more accurate approximation of the MRT

based on time-varying fixed effects specifications. However, the introduction of time varying

fixed effects in models 6 and 7 does not improve the accuracy of the estimate. In Model 6, the

average impact is significantly lower (6.71) than our benchmark, and the variability of the

estimates increases. Since the trade of the preferential policy is slightly underestimated, it

appears that the time-varying fixed effects in addition to the MRT also tend to absorb part of

the trade policy effect.

Things get even worse in the case of Model 7 which provides the most complete

specification of the fixed effects structure. The mean of the estimated impacts is negative but

the distribution presents a very large standard deviation (around 933), However, the central

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value is 8.72, much higher respect to results of previous models. Apparently, the country-

product-time dummies lead to very unrealistic estimates, likely due to high multicollinearity.

3.4 Results for preference dummy

In order to shed some light on the capability of the dummy variable to proxy the policy

effect, we use the bilateral trade flows generated by equation (5) and re-run the regression

including a dichotomous policy variable, , instead of ln( , ). In Table 4

we show the descriptive statistics of the estimated impact of the preference dummy.

Under the assumption that all variables are known, Model 1 generates an estimated

coefficient of the dummy variable equal to 0.220 on average. The results for Model 1 in Table

1 and Table 3 are not comparable: the estimated coefficient of the policy dummy represents

the total effect, while the estimated effect size of the preference margin represents the

marginal one (elasticity). However, the policy dummy cannot provide an accurate assessment

of policies that, by definition, often discriminate among countries and products, and this is

likely to lead to a large overestimation of the impact of preferential schemes. Moreover,

results are characterized by a high coefficient of variation implying a considerable risk of

under/overestimating the trade policy impact.

Table 3: Estimated coefficients of the policy variable: preference dummy. The omission of

MRT

Policy Variable: dummyPrefk

ijt MODEL 1 MODEL 2

Simple mean 0.22 0.50

Std. Deviation 0.22 0.38

Median 0.22 0.49

5th

percentile -0.09 -0.04

95th

percentile 0.55 1.06

Notes: Statistics of the distribution of estimated coefficients obtained using Heckman two-step Model.

Dependent variable: ln (X , , ). All independent variables are specified in eq. (6), dummypref , instead of

ln(pref , ). In models 2 multilateral price indices are excluded (eq.(7)), dummypref , instead of ln(pref , ).

Time Dummies included in all models. Simulations with 10.000 replications.

When we include , instead of ln( , ) in equation (7), it is still the case

that the omission of the MRT leads to an overestimation of the policy impact (Model 2 in

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Table 4). On the other hand, in this case the introduction of the time invariant fixed effects

does not lead to more accurate estimates. Table 4 shows that the specifications provided by

models 3, 4 and 5 lead to results that are not significantly different from those of Model 2

(with a statistically significant level of 1% )

Table 4: Estimated coefficients of the policy variable: preference dummy with FE

Policy Variable: dummyPrefk

ijt MODEL 3 MODEL 4 MODEL 5 MODEL 6 MODEL 7

Simple mean 0.45 0.51 0.49 0.42 1.86

Std. Deviation 0.27 0.61 0.42 0.30 135.65

Median 0.45 0.51 0.49 0.42 0.50

5th

percentile 0.01 -0.44 -0.17 -0.07 -10.90

95th

percentile 0.90 1.50 1.18 0.90 12.57

Importer Yes

Exporter Yes

Product Yes Yes Yes Yes

Importer*Product Yes

Exporter*Product Yes

Importer*Exporter Yes

Importer*time Yes

Exporter*time Yes

Importer*product*time Yes

Exporter*product*time Yes

Notes: Statistics of the distribution of estimated coefficients obtained using Heckman two-step Model.

Dependent variable: ln ( , , ). All independent variables are specified in eq. (8), , instead of

ln( , ). Time Dummies included in all models. Simulations with 10.000 replications.

The situation does not improve even when we introduce the time-varying dimension: the

average impact is still significantly overestimated in Model 6, while it is confirmed that the

full structure of time varying fixed effects in Model 7 is marred by high collinearity and leads

to an unrealistic overestimation of the average impact.

4. Conclusions

The assessment of the impact of trade policies on trade flows is at the hearth of a large

literature using the gravity model. Given the large volume of data available to gravity

15

modellers, many different specifications of the gravity equation can be “made to work" in the

sense that they generate statistical tests that tend to corroborate the specification’s validity.

More specifically, the majority of the recent significant contributions on the matter employs

exporter and importer fixed sector-specific effects. We use Monte Carlo experiments to show

that such a choice, together with measurement errors about the policy treatment, leads to bias

in the estimates of the policy impact.

This paper uses hypothetical but plausible data from a known data-generating process to

evaluate which models most closely and frequently draw correct conclusions from the

underlying structure of the data. In the gravity model literature, it has become increasingly

common to include fixed effects to account for the MRT. Our main contribution is to point

out that the identification of trade policy effects with a gravity equation that includes fixed

effects to control for the multilateral trade resistance terms has limitations. This is especially

true if the policy under investigation is not accurately measured: in such a case, the usual

fixed effects fix for the omitted (MRT) variable problem could make the consequences of the

measurement error even worse.

On the one hand, our results confirm that omission of a crucial variable such as

multilateral resistance causes an inaccurate assessment of the policy impact In particular (in

Model 2), the trade effect of preferences is on average overestimated if a continuous variable

is used, as well as if the policy is measured by a dummy. On the other hand, when we control

for country-product and time unobserved heterogeneity (Model 4), the estimated parameter

approaches the true (assumed) value of the policy treatment. As a matter of fact, this is true

only if the policy treatment is correctly measured by a continuous variable: fixed effects do

not solve the problem of the lack of the MRT when we have an error in the measurement of

the policy variable (Table 4).

The most striking result is that introducing time varying fixed effects (i.e. the complete

specification to proxy for the MRT) worsens the accuracy of the estimate of the policy

variable. Apparently, the more we control for time varying fixed effects, the more the

estimated parameter is biased (models 6 and 7) since the range of the estimates is greatly

inflated.

The bottom line is that a full-blown fixed effects specification risks to severely limit the

assessment of trade policy effects.

The situation is even worse if we proxy a policy variable with a dummy instead of a

continuous one. This amounts to combine a (policy) measurement problem with a (MRT)

omitted variable problem: in such a case any attempts to control for heterogeneity through a

16

fixed effect design would prevent us from evaluating trade policy effects due to the presence

of high collinearity.

17

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APPENDIX

Table A1. Descriptive statistics: Initial dataset.

Variable Mean St. dev. Min Max

Bilateral flow of trade (1000$) 42,528 253,218 0 13,700,000

Production (1000$) 3,313 7,065 0.001 75,229

Expenditure (1000$) 32,646 70,724 96 698,130

Distance 6,856 4,890 260 18,310

Language 0.05 0.22 0 1

Border 0.04 0.20 0 1

Exporter Price index 1.04 0.18 0.42 3.17

Importer Price index 1.03 0.09 0.5215 1.55

Preference margin 1.05 0.16 1 4.91

Preference dummy 0.80 0.40 0 1

Notes: Number of Obs. 21,896. Descriptive statistics are calculated on variables in levels.